The analysis and display of musical pitch information can provide invaluable feedback for musicians, singers, and the like. To better understand the present invention, it is necessary to define clearly what is meant by musical pitch. All musical sounds which have a perceivable pitch consist of a sound pressure waveform that is periodic in time. The simplest periodic waveform is the sine wave. Any number of harmonics (sine waves with frequencies which are integer multiples of the fundamental frequency) may be added to the basic sine wave to give a very complex waveform in the time domain. Even though these harmonics are present, we still perceive the pitch of the sound as the fundamental frequency of the waveform. In fact, if the fundamental frequency of a musical sound is weak or missing altogether, the human mechanism of pitch detection is able to infer the fundamental pitch from the harmonics that are present. Simple pitch measuring devices which are based in the frequency domain respond to all the frequencies present in the waveform and often yield ambiguous results. Even if a method is used to display the lowest frequency present, this frequency may not be the perceived pitch of the sound if the energy of the component at the fundamental frequency is much weaker than several of the harmonics.
A much better method of extracting the preceived pitch is to measure the period of time over which the waveform is periodic. This technique seems to more closely model the human mechanism of pitch detection. There are, however, pitfalls in this method. First, in naturally occurring acoustic sounds the frequency of the overtones or partials are often not exact multiples of the fundamental frequency, and therefore cannot accurately be called harmonics. This inexactness results in such waveforms having a dynamically changing structure in the time domain with the phase of the overtones constantly changing with respect to the phase of the fundamental frequency. Thus the shape of the waveform may be completely altered over a span of several cycles, while the shape of adjacent cycles remains quite similar. In addition, the overtone structure of musical sounds often changes dramatically over a relatively short period of time, especially in the case of human voice. This again causes the shape of the waveform to change over a span of several cycles.
Further complicating the measurement problem is the fact that naturally occurring acoustic waveforms tend to be modulated by random fluctuations in amplitude. Periodic amplitude and frequency fluctuations may also be present; i.e., tremolo and vibrato. The human singing voice usually has all three of these effects present to some degree.
No previous pitch measurement method has addressed all of these problems successfully. Many have realized the shortcomings of operating in the frequency domain and have chosen to attempt to measure the period of the waveform in the time domain. Most methods, such as Merrit in U.S. Pat. No. 4,028,985, and Slepian and Weldon in U.S. Pat. No. 4,217,808 rely on detecting amplitude peaks of the periodic waveform. There are several weaknesses to peak detection approaches. First, acoustic waveforms rich in overtones may have several peaks in one cycle, with the shape and amplitude of these peaks constantly changing as indicated in the above paragraphs. Thus, the peak that is detected in one cycle may not correspond to the peak in an adjacent cycle and gross measurement errors will result. Similarly, rapid random or periodic amplitude fluctuations may cause a peak to be missed or cause minor peaks to be mistaken for the major peak. Even if peaks are not missed, small amplitude variations may translate into substantial time measurement errors, since a waveform typically has a gentle slope near its peak.
In addition, most techniques that use the amplitude of the waveform require an Automatic Gain Control (AGC) circuit to accommodate changes in input signal level. To avoid distortion of the waveform, AGC circuits are designed to have a fast attack time and slow decay time. This prevents the circuits from tracking small rapid changes in amplitude present in naturally occurring acoustic waveforms. In normal audio applications this is not a problem, since the sound is judged only by the human ear which is not sensitive to moderate amplitude changes. However, small amplitude changes can cause peak detectors to make gross errors. Reducing the AGC decay time allows the circuit to track more rapid amplitude fluctuations, but causes level-dependent distortion of low frequency waveforms. To minimize these difficulties either the range of pitches that can be measured must be limited, or some means must be provided for adjusting the time constant of the AGC in concert with the incoming pitch.
It is a known technique to analyze frequency by measuring the times at which the waveform crosses zero. The zero-crossings of a waveform are completely unaffected by the waveform amplitude. While this technique is suitable for relatively pure tones, it presents problems for a waveform which may cross zero several times during a cycle. While some sort of filtering scheme can be used to remove the overtones so that only two zero crossings occur in one cycle, this requires either operator intervention or an automatic filtering scheme which would have all the undesireable characteristics of an AGC circuit. Thus, while the known zero-crossing technique avoids the problems presented by the peak amplitude technique, it is itself subject to other problems.